Mathematics at Chartres Cathedral
By Richard Stout
Journal of the ACMS, No.1 (2004)
Introduction: Having had several opportunities to travel to France, often with groups of students, our trips have usually included a visit to Chartres, especially to visit the magnificent Gothic cathedral that dominates the town. On a recent visit I was again struck by the beauty, majesty and awe that the cathedral inspires. The building not only does a remarkable job of telling Biblical stories and of enclosing a space conducive to worship, it directs one’s eyes and one’s spirits upward. This is achieved not only by the beautiful stained glass windows and the striking sculptures, but also by the overall design and proportions of the structure. When I returned home I thought it would be interesting to read more about the cathedral. It was then that I discovered that, in at least some authors’ minds, mathematics, particularly geometry, had a central role to play in the design and construction of the building. It is this contribution of mathematics that I would like to share in this paper.
The town of Chartres is located approximately 50 miles southwest of Paris. There has been a church in Chartres since the eighth century, however, it was in 876 that the town and its church became an important site. In that year Charles the Bald, grandson of Charlemagne, made a gift to the church at Chartres of the Sancta Camisia, a relic that was believed to be the veil or tunic worn by Mary when she gave birth to Christ. From that time on the church not only served to meet the religious needs of the townspeople, it was also used to house this relic and to accommodate great numbers of pilgrims who would come to Chartres to pay homage to the veil. Because of this relic, the church took on a special connection to the Virgin Mary.
In the Middle Ages, the town of Chartres was also an important seat of learning. In 990 a scholar named Fulbert came to Chartres and started a school which would rank as one of Europe’s leading scholastic institutions for the next 200 years. As Malcolm Miller points out in his booklet, “Chartres Cathedral”, the liberal arts were prominent in the school. Quoting the scholar Thierry of Chartres Miller notes, “Philosophy has two principal instruments, the mind and its expression. The mind is enlightened by the Quadrivium (arithmetic, geometry, astronomy, and music), its expression, elegant, reasonably ornate, is provided by the Trivium (grammar, rhetoric and dialectic).” Todaythere is a visual reminder of the school and the importance of learning amid the sculptures of the cathedral. The Royal Portal, located at the base of the western wall of the cathedral, is the entrance that most people use. Of the three bays that comprise this entrance, the right bay is dedicated to Mary. Above the door, the Tympanum tells the story of Mary. These sculptures are in turn surrounded by symbols for each of the seven liberal arts, along with a sculpture of a famous practitioner for each. Interestingly, Pythagoras is included as one of these practitioners